Monotonicity properties of the Neumann heat kernel in the ball ☆ [☆] The authors kindly acknowledge the support from CNCSIS - UEFISCSU research grant PNII - IDEI 209/2007.

Abstract: A well-known conjecture of R. Laugesen and C. Morpurgo asserts that the diagonal of the Neumann heat kernel of the unit ball is a strictly increasing radial function. In this paper we use probabilistic arguments to settle this conjecture and to prove some inequalities for the Neumann heat kernel in the ball. [ABSTRACT FROM AUTHOR]